|
|
A160296
|
|
Numerator of Hermite(n, 19/30).
|
|
1
|
|
|
1, 19, -89, -18791, -236879, 29323099, 1090116631, -58460151311, -4544610262559, 124108949730979, 20763741608252551, -163979183232607031, -105896125442269661039, -1126538793947045592341, 598088096752283650823671, 18460868240159776597398049
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 15^n * Hermite(n, 19/30).
E.g.f.: exp(19*x - 225*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(19/15)^(n-2*k)/(k!*(n-2*k)!)). (End)
|
|
EXAMPLE
|
Numerators of 1, 19/15, -89/225, -18791/3375, -236879/50625, ...
|
|
MATHEMATICA
|
Numerator[HermiteH[Range[0, 20], 19/30]] (* Harvey P. Dale, Sep 10 2011 *)
Table[15^n*HermiteH[n, 19/30], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
|
|
PROG
|
(PARI) x='x+O('x^30); Vec(serlaplace(exp(19*x - 225*x^2))) \\ G. C. Greubel, Oct 03 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(19/15)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 03 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign,frac
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|